Tính giá trị của biểu thức sau:7+7+7+7
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\(A.sin\dfrac{\pi}{7}=sin\left(\dfrac{\pi}{7}\right)cos\left(\dfrac{\pi}{7}\right)cos\left(\dfrac{2\pi}{7}\right)cos\left(\dfrac{4\pi}{7}\right)\)
\(=\dfrac{1}{2}sin\left(\dfrac{2\pi}{7}\right)cos\left(\dfrac{2\pi}{7}\right)cos\left(\dfrac{4\pi}{7}\right)\)
\(=\dfrac{1}{4}sin\left(\dfrac{4\pi}{7}\right)cos\left(\dfrac{4\pi}{7}\right)\)
\(=\dfrac{1}{8}sin\left(\dfrac{8\pi}{7}\right)\)
\(=\dfrac{1}{8}sin\left(\pi+\dfrac{\pi}{7}\right)=\dfrac{1}{8}sin\left(-\dfrac{\pi}{7}\right)\)
\(=-\dfrac{1}{8}sin\left(\dfrac{\pi}{7}\right)\)
\(\Rightarrow A=-\dfrac{1}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4/7.(8/-13)+4/7(-2/13)+1 3/13(-4/7)
= 4/7(-8/13-2/13+1)
=4/7. 3/13 =12/91
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(B=\left(1-\frac{1}{7}\right)\left(1-\frac{2}{7}\right)\left(1-\frac{3}{7}\right)...\left(1-\frac{2011}{7}\right)\)
\(B=\frac{6}{7}.\frac{5}{7}.\frac{4}{7}....\frac{-2004}{7}\)
Còn lại bạn tự tính đi.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{7}{1.2}+\dfrac{7}{2.3}+\dfrac{7}{3.4}+...+\dfrac{7}{2011.2012}\)
\(A=7\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2011.2012}\right)\)
\(A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2011}-\dfrac{1}{2012}\right)\)
\(A=7\left(1-\dfrac{1}{2012}\right)=7.\dfrac{2011}{2012}=\dfrac{14077}{2012}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đ=(12/6+7/8)-(-7/8+12/6)
Bỏ ngoặc
\(Đ=\frac{12}{6}+\frac{7}{8}+\frac{7}{8}-\frac{12}{6}\)
\(Đ=\left(\frac{12}{6}-\frac{12}{6}\right)+\left(\frac{7}{8}+\frac{7}{8}\right)\)
\(Đ=0+\frac{7}{4}\)
\(Đ=\frac{7}{4}\)
Ta có:7+7+7+7=7x4=28
Đ/S:28